Abstract
In this paper the steady planar travelling waves in the adiabatic model with two-step chain branching reaction mechanism are investigated numerically. The properties of these solutions are demonstrated to have similarities with the properties of non-adiabatic combustion waves that is, there is a residual amount of fuel left behind the travelling waves and the solutions can exhibit extinction. It is also shown that the model possesses a new type multiple travelling wave solutions (which we call wave trains) with complex structure of the profiles and varying speeds
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